Hi

I was attempting an Optimization question but I just do not know how to start it.

A man in a row boat, 5km from the nearest point on a straight shoreline, wishes to reach a point 12kms further down the shore. If he can row at the rate of 4kms per hour and run a rate of 6kms per hour, what course should he follow to reach his destination in the minimum time?

I first started the answer by drawing a triangle and one co-ordinate for the man in the boat, another co-ordinate for the shoreline, and the last co-ordinate for the nearest point.

How would i start attempting this question? I am not asking for just an answer, I want to know what my formula should start off like, and when I should derive, etc.

Thanks in advance.